Question

As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction mile in front of her. After she passes him, she can see him in her rear mirror until he is mile behind her. Emily rides at a constant rate of miles per hour, and Emerson skates at a constant rate of miles per hour. For how many minutes can Emily see Emerson?

Answer 1

Emily can see Emerson for 15 minutes.

Explanation:

As the values of speed and distance are missing in given question so we consider complete statement attached in Figure below.

Speed of Emily = 12 mile/hr

Speed of Emerson = 8 mile/hr

Speed of Emily relative to Emerson = 12 - 8 = 4 mile/hr

Initial distance between them = 1/2 mile

After crossing Emerson, distance between them = 1/2 mile

Time for which we can see Emily is moving with relative constant speed (Vr) of 4 mile/hr and Emerson is not moving at all relative to her

`=(Dist)/(V_(r))\\\\=((1)/(2))/(4)\\\\=(1)/(8) hrs`

Total distance in which Emily can see Emerson = 1/2 + 1/2 = 1 mile

Time spend in reaching Emerson covering 1/2 mile = 1/8 hrs

Time Emily can see Emerson in rear mirror for 1/2 mile = 1/8 hrs

Total time
`=(1)/(8)+(1)/(8)`

`=(1)/(4) hrs\\\\=(1)/(4) (60 mins)\\\\=15 mins`